Digital communication, especially sound-wave digital communication in the water (underwater acoustic digital communication), has problems to be solved such as interference from multipath waves, noises, restriction on bandwidth that can be used, and restriction on transmission level of waves that can be sent by a wave transmitter. One of the biggest problems among them is effects of the Doppler shift caused by a communication device (transmitter or receiver) on the move at a transmitting side or a receiving side.
A technique of phase compensation by a DPLL (Digital Phase Locked Loop) circuit, which is incorporated in an adaptive equalizer, has been applied to the effects of the Doppler shift. However, filtering by the adaptive equalizer can not sufficiently react to the Doppler shift caused by a fast moving speed. This is because timing of extracting symbols is shifted from a desired position due to the effects of the Doppler shift.
Therefore, further compensation is carried out for the timing error by re-sampling data with an interpolation filter, (as discussed, for example, in Patent Documents 1 (Japanese Translation of PCT International Application Publication No. 2012-528521) and 2 (Japanese Patent Application Publication No. 2013-038505), for example). However, the interpolation is merely made between data points, that is, approximation to obtain inaccurate data to be exact, and the processing uses such as a fixed FIR filter to fail to react for a case where the Doppler shift varies by time. A technique such as switching a filter has been conceived to react to the variation by time, but the result is that tracking capability is insufficient and computational load is increased due to switching of the filter.
As a result, no application example in underwater acoustic digital communication has been successful in reacting to a moving speed faster than several meters per second, as disclosed in Non-Patent Documents 1 (M. Johnson, L. Freitag and M. Stojanovic, “Improved Doppler Tracking and Correction for Underwater Acoustic Communications,” in Proc. ICAASP'97, Munich, Germany, pp. 575-578) and 2 (B. S. Sharif, J. Neasham, O. R. Hinton and A. E. Adams, “A computationally efficient Doppler compensation system for underwater acoustic communication,” IEEE J. Oceanic Eng., Vol. OE-25, pp. 52-61, 2000).